XXX-X-XXXX-XXXX-X/XX/$XX.00 ©20XX IEEE Modeling PV Modules Using Simulink / MATLAB under Varying Conditions Aleck W. Leedy Institute of Engineering Murray State University Murray, KY 42071, USA e-mail: aleedy@murraystate.edu Muhammad Abdelraziq Institute of Engineering Murray State University Murray, KY 42071, USA e-mail: mabdelraziq@murraystate.edu Abstract— Studying the behavior of PV modules under varying conditions is essential, due to the various environmental conditions that can affect the performance of the PV module. In this paper, basic functions in Simulink / MATLAB are used to model a 36-cell-50W PV module (solar panel) manufactured by AMERESCO Solar. Experimental measurements were acquired from the AMERESCO solar panel that were compared with the theoretical results obtained from the Simulink model. For the sake of simplicity, and without the loss of generality; a 5- parameter mathematical model of the PV module is used to model the PV module of interest. Since the purpose of most PV module simulations is to study the P-V and I-V characteristics of the PV module, detailed P-V and I-V curves are generated from the Simulink model and compared with their counterparts provided by AMERESCO (in the manufacturer manual). This paper will also present a brief and basic attempt of studying partial shading in single PV modules. Keywords - 36-cell PV module; PV characteristics; maximum power point tracking; partial shading. I. INTRODUCTION The considered PV module model is called a static model. A static model is a model best suited for slow variations in solar irradiance and load. On the other hand, a dynamic model is needed in several situations where a precise knowledge of the PV cell behavior during transient effects is required [1]. Following the static model representation of the PV cell, the total current can be expressed by the following relationship [1]:                      1 1 2 2 1 kT qV S kT qV S ph e I e I I I (1) where I is the PV cell terminal current, V is the PV cell terminal voltage, K is the Boltzmann constant in J/k, q is the fundamental charge of the electron in C, T is the PV cell temperature, IS1 is the dark saturation current of the first diode, IS2 is the dark saturation current of the second diode, Iph is the photo-generated current that is linearly dependent on solar irradiance. The photo-generated current can be expressed as:            0 0 r r ph ph I I I I (2) where Ir is the light intensity (irradiance) in 2 m W incident on the PV cell, 0 ph I is the measured solar-generated current for a chosen reference 0 r I (usually 2 1000 0 m W I r  ). Equation (2) can be obtained by applying Kirchhoff’s current law on the circuit given in Fig.1. The first diode has an ideality factor of 1, while the second diode has an ideality factor equal to 2. In practicality, the ideality factors of the two diodes are unlikely to be equal to the values 1 and 2 [1]. Therefore, (1) is modified to a more generic form as follows [1, 2]:   P s kT N qV S kT N qV S ph R IR V e I e I I I                        1 1 2 1 2 1 (3) where N1 and N2 are the quality factors for the first and second diodes respectively. The values for the quality factor vary with accordance to the material from which the PV cell is manufactured. Tabulated values can be easily found in other literature [3]. The quality factor is typically 2 for polycrystalline cells, and varies for amorphous cells [3]. Equation (2) is the generalized double diode model for the PV cell, with an equivalent circuit shown in Fig. 2 [1]. To model the series power losses due to the flow of current through different parts of the PV cell, the value of Rs accounts for such losses to a good extent [1]. The series resistance reduces the short circuit current, moreover, it has no effect on the circuit voltage. It is important to note that Rs affects the Fig. 1. PV cell circuit model.